**1. Introduction**

Conventional synchronous generators store kinetic energy in their rotor shaft and provide inertia to the system. The frequency of the power system is directly coupled to the rotational speed of the generator. Therefore, more rotational inertia may lead to a stable power system. Recently, the installation of renewable resources in the power system has increased. These resources are integrated into the power system using power converters, but they do not provide rotating inertia to the power system. High penetration of distributed energy resources (DER) might create instability if not properly controlled. Therefore, ancillary functions had to be added and must be achieved by the controllers of the DER. Renewable resources can provide voltage regulation and frequency support if controlled properly.

For instance, the wind energy system (WES) can be adjusted to provide frequency support by controlling the injected active power as a function of frequency. To do so, WES must maintain a certain reserve of active power, and then the reserved power can be utilized during a frequency drop.

The active power control (APC) during a disturbing condition is a challenge when it is applied to a wind farm. The APC requires a fast dynamic response range in a few seconds. Active power control involves three main sub-control objectives in a power system: the inertial control, the primary frequency control (PFC), and automatic generation control (AGC) [1,2]. Each is involved in the control of active power for a certain time in sequence order due to their timely response. One main challenge is that wind availability is uncertain, causing failure in the control loop due to wind speed variation.

Participating in frequency control can be implemented by adjusting the conventional control techniques of WES systems [1–14]. Different control methods, and approaches have been implemented to adjust the frequency of a power system during frequency fluctuation [15,16]. These control strategies can be classified based on the capability and duration of participation [15–19]. The first approach is to use the stored kinetic energy to be implemented as inertial control. The stored energy can be released for a few seconds depending on the inertia of the turbine. The other control is to de-load the wind turbine below the maximum power point, providing a long-term power supply following the inertial response to maintain a new steady state value of frequency. This is known as a primary frequency response (PFC). There have been several studies on implementing the PFC in power systems with existing wind turbines. Some studies have focused on the wind farm level, whereas others have focused on the power system level [20–23]. Also, some studies have analyzed the equivalent damage loads for de-loaded wind turbines [24]. Other researchers have focused on the reserve methods and the response of the wind turbines to PFC [25–28].

In reference [29], the active power control strategy was performed for a WES using inertial, PFC and AGC. Different droop control approaches were proposed to support the frequency of the grid. Variable droop controller was proposed to enhance the response of WES based on doubly fed induction generator DFIG in reference [30]. The concept of droop can be implemented in the local controller of the WES, at the wind farm level, or to the coordinated distributed generator in the smart grid [31–40].

In this article, a fuzzy logic-based controller is developed for the WES to provide frequency support for a smart grid. The controller is designed to identify the participation factor of each wind turbine based on the reserved power and the ROCOF at the point of common coupling (PCC).

A power system is developed to test the response of the wind farm to the frequency drop.

### **2. Stability of the Power Grid**

A power system is a complicated structure involving various elements with different dynamics. In the ideal world, loads of the power system are provided with consistent frequency and voltage. At normal conditions, all synchronous generators are synchronized to avoid up-normal fluctuation in the voltage and current, which may lead to disconnecting areas from the grid. The frequency deviation is a result of an imbalance between the load and power generated. The frequency of the gird is related to the rotor speed of the synchronous generators of the power system. The change of frequency of a network can be given as [41]:

$$
\Delta f = \frac{1}{\left(2H\_{sys}\right)S + D\_{sys}} \left(\sum \Delta P\_G - \sum \Delta P\_L\right) \tag{1}
$$

where *Hsys* and *Dsys* are the equivalent inertia and damping constants of all machines of the system. The change in generated power and load power are represented by Δ*PG* and Δ*PL* respectively. To ensure stability, the synchronous generator should be equipped with a droop curve in the speed controller of the turbine's torque-speed characteristic. The droop characteristic is typically set to 5% in the United States [42].

### **3. Frequency Support by a Wind Energy System**

WES can be controlled to maintain certain reserve power and then, it can be used to provide APC by modifying the control loop to follow the required power reference. To do so, a droop control concept is implemented where the active power is related to the frequency of the grid.

The required active power to stabilize the grid frequency can be achieved by implementing the droop curve. The response of WES during frequency drop depends substantially on the de-loading method used to maintain the reserve power (i.e., rotor speed or pitch angle). Also, the response of the WES can be impacted by the initial operating points of WES just slightly before the occurrence of frequency deviation. Thus, the droop curve has to be selected cautiously to guarantee stability and

reliable response of WES. For instance, very fast droop for a de-loaded WES that operates away from its maximum point may lead to controller instability [43,44].

The droop curve that implemented in the synchronous generator can be adapted to be used for WES. The variation in the active power of a WES can be expressed as [35]:

$$P\_{PFC} = \frac{P\_{\text{WT,arcu}}}{R} \frac{(f\_{\text{nom.}} - f\_{\text{grid}})}{f\_{\text{nom.}}} \tag{2}$$

where *PWT*,*ava* is the maximum power available that can be generated by the WES. *fgrid* is the measured grid frequency; and *fnom*. the nominal grid frequency are represented respectively. Here, R is defined as the slope of the droop curve represented in percentage. The slope determines the rate of power change in WES. Small droop rate means a fast change in active power. Figure 1 demonstrates di fferent droop curves as function of an active power change in percentage.

**Figure 1.** The change of power for di fferent droop rates.

The rate of the droop controller must be selected to ensure a reliable and smooth response against the deviation of the grid's frequency. Designing the droop curve for frequency regulation depends on the initial state and the power availability of the WES. Because of the variation of wind speed, the active power produced by WES is variable. As a result, the amount of the power reserve for WES is also dynamic. Also, the ROCOF at the PCC varies depending on how much power is lost from the network. Therefore, for WES a dynamic controller is the best fit to provide adjustment to the grid's frequency.
